Numerical Analysis of Ordinary and Delay Differential Equations

This book is a concise textbook for students in advanced undergraduate or first-year graduate courses in applied mathematics, control, and engineering who want to understand the modern standard of numerical methods for ordinary and delay differential equations. It also covers the recent developments in numerical analysis of these differential systems and introduces the asymptotic stability of analytical and numerical solutions.

Format: Paperback / softback
Length: 113 pages
Publication date: 06 April 2023
Publisher: Springer Verlag, Singapore

This book serves as a comprehensive textbook for students enrolled in advanced undergraduate or first-year graduate courses in diverse disciplines such as applied mathematics, control, and engineering, who seek to gain a deep understanding of the modern standard of numerical methods for ordinary and delay differential equations. Moreover, experts in these fields can also explore the latest advancements in the numerical analysis of such differential systems.

Ordinary differential equations (ODEs) possess immense mathematical power, enabling them to effectively describe a wide array of phenomena across science and engineering. Alongside their inherent significance, one of the remarkable directions in which ODEs evolve is their integration with an unknown function possessing a delayed argument. This concept is known as delay differential equations (DDEs), which frequently arise in mathematical modeling of biology, demography, epidemiology, and control theory. In certain instances, the solution of a differential equation can be obtained through algebraic combinations of known mathematical functions. However, in many practical scenarios, such a solution proves elusive or unattainable, necessitating the use of numerical approximations. The advent of modern computers has further accelerated this situation, opening up new possibilities for numerical methodologies. Consequently, the knowledge and expertise of numerical solutions for differential equations have become essential requirements in various fields of science and engineering. It may be tempting to believe that well-organized software packages like MATLAB serve as equivalent solutions. In a sense, this is true; yet, it is crucial to bear in mind that the indiscriminate employment of software packages can lead to misinformation. The core essence of numerical solutions for differential equations remains a subject that requires thorough learning.

The present book aims to provide a concise yet comprehensive introduction to the numerical solutions of ordinary differential equations. It serves as a valuable resource for students, scholars, and practitioners seeking to delve into this field. By presenting the fundamental principles, techniques, and applications of numerical methods, this book equips readers with the necessary skills and knowledge to solve complex differential equations and apply them to real-world problems. Whether you are a student embarking on your academic journey or an experienced professional seeking to advance your expertise, this book will be an invaluable companion on your path to understanding and applying numerical solutions for differential equations.

Weight: 226g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811992629
Edition number: 1st ed. 2023